Download Fractions, Decimals, and Percents

Fractions, Decimals, and Percents
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
____
____
1. Write 1.166 in expanded form.
a. 1 + 0.1 + 0.6 + 0.6
c. 1 + 0.1 + 0.06 + 0.006
b. 1 + 1 + 6 + 6
d. 1 + 0.01 + 0.006 + 0.0006
2. Write 4 + 0.6 + 0.05 + 0.009 in standard form.
a. 4.6509
c. 4.0659
b. 40.659
d. 4.659
3. Write 11.2 in words.
a. two tenths
c. eleven and two hundredths
b. eleven and two tenths
d. two hundredths
4. Order the following decimals from least to greatest.
2.518, 2.287, 2.611
a. 2.287, 2.518, 2.611
c. 2.518, 2.287, 2.611
b. 2.287, 2.611, 2.518
d. 2.611, 2.287, 2.518
5. Find the product.
4.17 • 4.6
a. 8.77
c. 19.182
b. 191.82
d. 1.9182
6. Find the quotient.
____
a. 0.234
b. 2.34
7. Divide.
____
____
____
____
____
c. 23.4
d. 2.68
a. 0.098
c. 9.8
b. 0.98
d. 1.020408163265
8. Write the decimal 2.32 as a fraction or mixed number.
a. 2 8
c. 1
25
b.
16
d. 2 3
10
8
25
____
9. Write the number
1
8
as a decimal.
a. 18
c. 0.09
b. 0.125
d. 0.08
____ 10. Order the fractions and decimals from least to greatest.
0.58, 0.8,
a.
2
3
2
3
, 0.58, 0.8
b. 0.58, 2 , 0.8
3
____ 11. Find two equivalent fractions for .
c. 0.8, 2 , 0.58
3
d. 0.58, 0.8,
2
3
a.
and
c.
and
b.
and
d.
and
____ 12. Find the missing number that makes the fractions equivalent.
a. 8
b. 12
c. 6
d. 2
____ 13. Write the fraction
in simplest form.
a.
c.
b.
d.
5
1
____ 14. Order 6 , 5 , and
a.
1
b.
3
5
, 4,
1
5
, 6,
5
3
4
from least to greatest.
c.
5
6
d.
3
4
5
3
6
, 4,
3
1
4
, 5,
1
5
5
6
____ 15. Subtract, and write the answer in simplest form.
7
38 –
5
8
a. 1 15
16
c. 4 1
2
b. 3 1
4
d. 1 5
8
____ 16. Multiply
a.
. Write the answer as a mixed number in simplest form.
c.
1
18
2
3
b. 3 1
6
d.
1
2
____ 17. Multiply the fractions, and simplify if possible.
1
•
8
5
7
a.
c.
5
29
b.
5
56
d.
7
40
47
56
____ 18. Multiply the fractions, and simplify if possible.
4
15 
7
9
a. 2 26
45
c. 2 11
35
b. 1 2
5
d. 1 38
59
____ 19. Multiply the mixed numbers, and simplify if possible.
1
2
22  17
a. 3 11
14
c. 3 3
14
b. 1 17
18
d. 2 1
7
____ 20. Divide, and simplify if possible.
1
1
13  14
a.
c. 1 1
15
15
16
b.
d. 1 2
3
3
5
____ 21. Evaluate
a.
1
5
+ 8.
5
11
c.
34
d.
4
13
b.
39
33
40
5
2
2
____ 22. Evaluate 2 3 – 1 5 .
a. 1 4
15
c. 1 3
16
b. 1
d. 1 1
3
3
7
____ 23. Evaluate 2 7 – 1 12 .
a.
c.
b.
d.
71
84
71
83
____ 24. Write 30% as a fraction in simplest form.
a. 0.3
c.
10
3
b. 1
10
d.
3
3
10
____ 25. Write 96% as a decimal.
a. 0.96
c.
24
25
b. 1.04
____ 26. Write the decimal 0.08 as a percent.
a. 2
d. 9.6
c. 0.8%
25
b. 8%
____ 27. Write the fraction
d. 0.0008%
2
5
as a percent.
a. 250%
b. 4%
____ 28. Find 20% of 35.
a. 700
b. 7
Graph each number on a number line.
3
____ 29. 1 4
c. 40%
d. 0.4%
c. 175
d. 10.4
a.
c.
–5
–4
–3
–2
–1
0
1
2
3
4
5
b.
–5
–4
–3
–2
–1
0
1
2
3
4
5
–5
–4
–3
–2
–1
0
1
2
3
4
5
–5
–4
–3
–2
–1
0
1
2
3
4
5
–5
–4
–3
–2
–1
0
1
2
3
4
5
d.
–5
–4
–3
–2
–1
0
1
2
3
4
5
____ 30. 1.75
a.
c.
–5
–4
–3
–2
–1
0
1
2
3
4
5
b.
d.
–5
–4
–3
–2
–1
0
1
2
3
4
5
Find a fraction equivalent to the given fraction.
____ 31.
a.
c.
b.
d.
a.
c.
b.
d.
____ 32.
____ 33. Write
as a mixed number in simplest form.
a. 8 4
7
c. 8 5
7
b. 7 5
7
d. 7 6
7
5
____ 34. Write 5 6 as an improper fraction.
a.
35
c.
29
d.
6
6
b.
6
8
3
____ 35. Write the fraction
1
as a decimal. Round to the nearest hundredth if necessary.
a. 0.47
c. 0.27
b. 3.11
d. 3.67
____ 36. Write the decimal 6.64 as a mixed number in simplest form.
a.
c. 6 16
25
b.
____ 37. Which decimal is less than –3.79?
a. –3.78
b. –3.689
d. 6 16
25
c. –3.7889
d. –3.801
____ 38. Order the numbers from least to greatest.
1
–1.656, –1.75, 1 2
a. –1.656, –1.75, 1 1
2
c. –1.75, –1.656, 1 1
2
b. –1.75, 1 1 , –1.656
2
d. 1 1 , –1.656, –1.75
2
____ 39. Add. Estimate to check whether the answer is reasonable.
31.364 + 21.603
a. 52.967
c. 5.2867
b. 5.2967
d. 52.867
____ 40. Subtract. Estimate to check whether the answer is reasonable.
60.123  18.179
a. 78.202
c. 41.944
b. 78.302
d. 41.954
____ 41. Multiply. Estimate to check whether the answer is reasonable.
0.88 • 17
a. 1.506
c. 1.496
b. 15.06
d. 14.96
____ 42. Multiply. Estimate to check whether the answer is reasonable.
27.6 • (–11.5)
a. –317.3
c. –31.73
b. –317.4
d. –31.74
____ 43. Divide. Estimate to check whether your answer is reasonable.
29.9  (–23)
a. –1.3
c. 52.9
b. –1.387
d. –0.769
____ 44. Divide. Estimate to check whether the answer is reasonable.
23.184  (–8.28)
a. –2.8
c. 2.8
b. –0.28
d. 28
____ 45. Divide. Estimate to check whether the answer is reasonable.
52  3.25
a. –160
c. 1.6
b. 16
d. –16
____ 46. Multiply. Write the answer in simplest form.
8
1
3
a. 24
b. 1
24
c. 24
d. 8
3
____ 47. Multiply. Write the answer in simplest form.
2
5 
3
7
a.  14
15
c.  6
35
b.  2
35
d.  6
5
____ 48. Multiply. Write the answer in simplest form.
3
1
37 
a.
12
c. 3 1
2
2
7
b.
7
288
d. 41 1
7
____ 49. Divide. Write the answer in simplest form. If the quotient is greater than 1, write the answer as an improper
fraction.
2
÷
5
a.
1
5
c.
2
25
b.
25
2
d. 2
1
2
____ 50. Divide. Write the answer in simplest form.If the quotient is greater than 1, write the answer as a mixed
number.
10
3
1 11 ÷
4
a. 2
11
c.
b. 1 19
44
d.
6
11
28
44
63
____ 51. Perform the following operation, and then simplify, if possible.
a.
c.  5
8
3
8
b.
d.
5
16
5
8
____ 52. Perform the following operation, and then simplify, if possible.
a.
c.
2
15
5
18
b.  1
18
d.
5
6
____ 53. Add the mixed numbers.Write the answer as a mixed number in simplest form.
1
5
93 + 38
a. 12 11
12
c. 28 3
11
b. 12 23
24
d. 5 2
11
____ 54. Subtract the mixed numbers.Write the answer as a mixed number in simplest form.
2
3
37 – 35
a.  9
35
c.  11
12
b.  11
35
d. 2 1
2
____ 55. Write 8% as a fraction in simplest form.
a. 0.08
c.
25
2
b. 1 2
25
d.
2
25
____ 56. Write 14% as a decimal.
a. 7.14
b. 0.14
c. 1.4
d. 7
50
____ 57. Write the decimal 0.56 as a percent.
a. 5.6%
b. 0.0056%
____ 58. Write the fraction
____ 59.
____ 60.
____ 61.
____ 62.
3
4
c. 56%
d. 14 %
25
as a percent.
a. 0.75%
c. 133.33%
b. 0.75
d. 75%
Use a fraction to estimate 18% of 98.
a. 24
c. 2,000
b. 30
d. 20
Find 95% of 195.
a. 185.25%
c. 18,525
b. 205.26
d. 185.25
27 is what percent of 30? If necessary, round your answer to the nearest tenth of a percent.
a. 111.1%
c. 0.9%
b. 1.1%
d. 90%
48 is 30% of what number? If necessary, round your answer to the nearest tenth.
a. 4.9
c. 160
b. 62.5
d. 1.6
Short Answer
63. The floor of a house is 80% covered by carpeting.
a. Write the percent of the floor covered by carpeting as a decimal.
b. Write the percent of the floor covered by carpeting as a fraction in its simplest form.
64. Consider the numbers 5 , 5.2, 5.02, 5 , and 5.333.
a.
b.
Order the numbers from least to greatest.
Write each of the fractions as a decimal, and each of the decimals as a fraction in
simplest form.
65. Explain how to write 40% as a fraction in simplest form.
Essay
66. Assume you know that a hot-air balloon is currently inflated with a certain amount of air and that the amount
is a percent of the total amount required to inflate the balloon. Explain how you would determine the total
amount of air required to inflate the balloon.
67. Suppose you had money in savings accounts at two different banks. If the amount of money in the first
account is greater than the amount of money in the second account, can you assume that the first bank pays a
higher interest rate? If not, what information would you need to determine which bank pays the higher interest
rate?
68. If a tree grows during the course of a year, is its percent change an increase or a decrease? Explain how you
would determine the percent change.
Fractions, Decimals, and Percents
Answer Section
MULTIPLE CHOICE
1. ANS: C
Expand the digits of the decimal. For example, given the number 3.141, you will have 3 + 0.1 + 0.04 + 0.001.
KEY: decimal
NOT: /A/Is this number mathematically the same as the original? /B/Do you need to add a decimal point?
/C/Correct! /D/Are your leading zeros correct?
2. ANS: D
Example:
Given the number 3.141, you will have 3 + 0.1 + 0.04 + 0.001.
KEY: decimal
NOT: /A/Should the last digit be in the thousandths place or the ten-thousandths place? /B/Should the first
digit be in the tens place or the ones place? /C/Is the decimal in the correct place? /D/Correct!
3. ANS: B
Is there a number before the decimal? If so, write this number in word form. Place the word and between the
whole number portion and the decimal portion of the number. Write the numbers following the decimal in
words. Determine how many decimal places are present. Write the corresponding word for the decimal place.
KEY: decimal
NOT: /A/Is there a number before the decimal point? /B/Correct! /C/Check the place value of your decimal.
/D/Is there a number before the decimal point?
4. ANS: A
Working from left to right, compare the digits in each place to determine the order of the decimals.
KEY: decimal, compare, order
NOT: /A/Correct! /B/Compare each decimal place, working from left to right./C/Are you working from left
to right? /D/Are you comparing the proper numbers?
5. ANS: C
Multiply the two numbers. To determine the placement of the decimal point in the answer, count the number
of decimal places in the two numbers being multiplied. In the answer, place the decimal point that many
places from the right.
KEY: decimal, multiplication
NOT: /A/Should you add the numbers? /B/Did you count the decimal places in the problem to determine the
decimal-point placement in the answer? /C/Correct! /D/How many combined decimal places are in the two
numbers being multiplied?
6. ANS: B
Divide as you would with whole numbers, and place the decimal point in the quotient directly above the
decimal point in the dividend.
KEY: decimal, division
NOT: /A/Did you place the decimal point correctly in your answer? /B/Correct! /C/Did you place the decimal
point correctly in your answer? /D/Should you subtract?
7. ANS: B
To divide decimals, multiply the divisor and the dividend by the same power of ten to remove the decimal
point from the divisor. Place the decimal point in the quotient directly above the decimal point in the
dividend.
KEY: decimal, division
NOT: /A/Is your decimal point placed properly? /B/Correct! /C/Is your decimal point far enough to the left?
/D/Are you dividing by the correct number?
8. ANS: A
If there is a number to the left of the decimal, write that as the whole number. Write the decimal part as a
fraction over 100, and simplify.
KEY: decimal, fraction, mixed number
NOT: /A/Correct! /B/Are you sure about the whole number part of the answer? /C/Should the digits after the
decimal point be the denominator? /D/Is this an exact answer, or did you round to just one decimal place?
9. ANS: B
To write a mixed number as a decimal, keep the whole number, and divide the numerator by the denominator
for the part to the right of the decimal point.
KEY: fraction, decimal
NOT: /A/How do you write a fraction as a decimal? /B/Correct! /C/Should you add all of the digits?
/D/Should you multiply all of the digits?
10. ANS: B
Write all of the numbers as decimals with the same number of places. Order the numbers from least to
greatest by comparing the digits from left to right.
KEY: fraction, decimal, compare, order
NOT: /A/Correct! /B/Does the problem ask for the numbers to be ordered from greatest to least? /C/Did you
write each of the numbers as a decimal before trying to compare them?/D/Did you write each of the numbers
as a decimal with the same number of places so you could compare them?
11. ANS: C
Multiply or divide the numerator and denominator by the same nonzero number.
KEY: equivalent fraction
NOT: /A/Are these two fractions equal to each other? /B/Did you multiply or divide both the numerator and
denominator by the same number? /C/Correct! /D/Did you confuse the numerator and denominator by
inverting the fractions?
12. ANS: C
Multiply both the numerator and the denominator of the first fraction by the same number to obtain the
second fraction.
KEY: fraction, equivalent fraction, multiplication, division
NOT: /A/Did you multiply both the numerator and denominator by the same number to obtain the second
fraction? /B/Did you find the factor used to obtain the other number in the new fraction? Use it to find this
number as well. /C/Correct! /D/Can this number be the same as it was in the first fraction if the other number
has changed?
13. ANS: A
If the GCF of both the numerator and the denominator is 1, then the fraction is already in simplest form.
Otherwise, divide the numerator and denominator by the GCF to simplify it.
KEY: fraction, simplest form
NOT: /A/Correct! /B/Did you divide the numerator by the same number you used to simplify the
denominator? /C/This fraction is equivalent, but is it the simplest form? /D/Did you divide the denominator
by the same number you used to simplify the numerator?
14. ANS: A
First write the fractions so that they have a common denominator. Then order them from least to greatest by
comparing the numerators.
KEY: fraction, order
NOT: /A/Correct! /B/Did you compare the numerators of the fractions after writing them with common
denominators? /C/Did you put the fractions in order from least to greatest?/D/Did you write the fractions with
common denominators to compare them?
15. ANS: B
Subtract the numerators of the fractions and write the result over the common denominator. Then subtract the
whole numbers, and simplify if necessary.
KEY: fraction, like fraction, mixed number, subtraction
NOT: /A/Did you remember the rules for subtracting fractions? Subtract the numerators and keep the
denominator. /B/Correct! /C/Did you subtract the fractions or add them? /D/Did you remember that you keep
the common denominator when subtracting fractions?
16. ANS: D
Write the whole number as a fraction with a denominator of 1. Multiply numerators and denominators. Write
the answer in simplest form.
KEY: fraction, multiplication
NOT: /A/Did you write the whole number as a fraction over 1 and then multiply the numerators and the
denominators? /B/Did you multiply the whole number by the fraction, or did you add them together? /C/Did
you multiply the whole number by the numerator, or did you add them together? /D/Correct!
17. ANS: C
Multiply the fractions by multiplying the numerators and multiplying the denominators, and then simplify if
possible.
KEY: fraction, multiplication
NOT: /A/Is this how you multiply fractions? /B/Are you supposed to be dividing the fractions?/C/Correct!
/D/Are you supposed to be adding the fractions?
18. ANS: B
First write any mixed numbers as improper fractions, and then multiply the numerators and multiply the
denominators. Simplify if possible.
KEY: fraction, mixed number, multiplication
NOT: /A/Are you supposed to be adding the fractions? /B/Correct! /C/Are you performing the correct
operation? /D/Is this how you multiply fractions?
19. ANS: C
First write the mixed numbers as improper fractions, and then multiply the numerators and multiply the
denominators. Simplify if possible.
KEY: mixed number, multiplication
NOT: /A/Are you supposed to be adding the fractions? /B/Are you performing the correct
operation?/C/Correct! /D/Is this how you multiply fractions?
20. ANS: C
To divide fractions, first write any mixed numbers as improper fractions, and then multiply the first fraction
by the reciprocal of the second fraction. Simplify if possible.
KEY: reciprocal, fraction, division
NOT: /A/Did you use the reciprocal of the right fraction? /B/Are you using the reciprocal at the right time?
/C/Correct! /D/Are you performing the correct operation?
21. ANS: B
To add or subtract the fractions, first find the lowest common denominator and rewrite them as equivalent
fractions. Then add or subtract the numerators, and place the result over the common denominator.
KEY: fraction, addition, subtraction, unlike denominators
NOT: /A/Did you calculate your denominator correctly? /B/Correct! /C/Did you calculate the equivalent
fractions properly? /D/Did you calculate your numerator correctly?
22. ANS: A
Add or subtract the fractions by finding the lowest common denominator and rewriting them as equivalent
fractions. Add or subtract the fractions and then the whole numbers. Simplify.
KEY: mixed number, addition, subtraction
NOT: /A/Correct! /B/What must you do to the denominators when adding or subtracting fractions? /C/Did
you calculate your denominator correctly? /D/Did you calculate your numerator correctly?
23. ANS: C
First find the lowest common denominator, and rewrite the fractions as equivalent fractions. Then subtract 1
from the whole number of the first mixed number, and add a fraction equivalent to 1 to the fractional part of
the first mixed number to make the first numerator greater than the second. Finally subtract the whole
numbers and then the fractions.
KEY: mixed number, rename
NOT: /A/Did you find a common denominator? /B/Did you find a common denominator? /C/Correct! /D/Did
you calculate your denominator correctly?
24. ANS: D
Place the percent in the numerator of a fraction with 100 in the denominator. Then simplify the fraction.
KEY: percent, fraction
NOT: /A/Did you find the decimal value or the fraction? /B/What number should be placed in the numerator
of the fraction? /C/Which number goes in the numerator of the fraction? /D/Correct!
25. ANS: A
Divide the percent by 100.
KEY: percent, decimal
NOT: /A/Correct! /B/What number should you divide by? /C/Is this in decimal form? /D/What number
should you divide by?
26. ANS: B
Multiply the decimal by 100.
KEY: percent, decimal
NOT: /A/Should this be a fraction? /B/Correct! /C/What number do you multiply by? How many places do
you move the decimal point?/D/Do you multiply or divide in this case? Which direction do you move the
decimal point?
27. ANS: C
Divide the numerator by the denominator, multiply the result by 100, and place a % symbol behind the
answer.
KEY: percent, fraction
NOT: /A/Should you divide the numerator by the denominator or the denominator by the numerator? /B/How
many places should you move the decimal point? /C/Correct! /D/Did you forget to multiply by some number?
28. ANS: B
Multiply 35 by 20, then divide by 100.
KEY: percent, multiplication
NOT: /A/Did you forget to divide the percent by 100? /B/Correct! /C/Should you multiply the number by the
decimal form of the percent? /D/What is the decimal equivalent of the percent?
29. ANS: B
The point is between –2 and –1. Approximate where on the number line the fraction would be.
KEY: decimal, fraction, number line, rational number
NOT: /A/Decide between which two integers the fraction would be. /B/Correct! /C/Decide between which
two integers the fraction would be. /D/Pay attention to the fraction's sign.
30. ANS: A
The point is between 1 and 2. Approximate where on the number line the decimal would be.
KEY: decimal, fraction, number line, rational number
NOT: /A/Correct!/B/Pay attention to the sign. /C/Decide between which two integers the decimal would be.
/D/Decide between which two integers the decimal would be.
31. ANS: D
To find an equivalent fraction, multiply or divide both the numerator and the denominator by the same
number.
KEY: equivalent, fraction
NOT: /A/Did you multiply or divide the numerator and the denominator by the same number? /B/This is the
reciprocal of the fraction, not an equivalent fraction. /C/This is the opposite of the fraction, not an equivalent
fraction. /D/Correct!
32. ANS: D
To find an equivalent fraction, multiply or divide both the numerator and the denominator by the same
number.
KEY: equivalent, fraction
NOT: /A/Did you multiply or divide the numerator and the denominator by the same number?/B/This is the
reciprocal of the fraction, not an equivalent fraction. /C/This is the opposite of the fraction, not an equivalent
fraction. /D/Correct!
33. ANS: B
Divide the numerator by the denominator. Use the quotient and remainder to write the mixed number.
KEY: convert, improper fraction, mixed number
NOT: /A/Divide the numerator by the denominator. Use the quotient as the whole number, and put the
remainder over the denominator. /B/Correct! /C/Divide the numerator by the denominator. Use the quotient as
the whole number, and put the remainder over the denominator. /D/Divide the numerator by the denominator.
Use the quotient as the whole number, and put the remainder over the denominator.
34. ANS: A
Multiply the denominator and whole number, and then add the numerator. Write the result over the
denominator.
KEY: convert, improper fraction, mixed number
NOT: /A/Correct! /B/Multiply the denominator and the whole number, and then add the numerator. Put this
result over the original denominator. /C/Multiply the denominator and the whole number, and then add the
numerator. Put this result over the original denominator. /D/Multiply the denominator and the whole number,
and then add the numerator. Put this result over the original denominator.
35. ANS: C
To write a fraction as a decimal, divide the numerator by the denominator.
KEY: convert, decimal, fraction, rational number
NOT: /A/Be careful when dividing. /B/Divide the numerator by the denominator. /C/Correct! /D/Divide the
numerator by the denominator.
36. ANS: D
Use the place value of the decimal part of the number to calculate the fraction. For example, 6.25 is 6 and
since the decimal part of 6.25 goes out to the hundredths place. Simplify the fraction to obtain
.
KEY: convert, decimal, fraction, rational number
NOT: /A/This decimal number does not go out to the thousandths place. /B/The fraction part is not in
simplest form. /C/Pay attention to the sign. /D/Correct!
37. ANS: D
To compare decimals, line up the decimal points and compare digits from left to right until you find the place
where the digits are different. Remember to consider a negative sign.
KEY: compare, decimal
NOT: /A/Line up the decimal points and check from left to right until you find the place where the digits are
different. If the numbers are negative, remember that the number closer to zero on the number line is the
greater number. /B/Line up the decimal points and check from left to right until you find the place where the
digits are different. If the numbers are negative, remember that the number closer to zero on the number line
is the greater number. /C/Line up the decimal points and check from left to right until you find the place
where the digits are different. If the numbers are negative, remember that the number closer to zero on the
number line is the greater number. /D/Correct!
38. ANS: C
Write all of the numbers as decimals having the same number of places.
KEY: compare, decimal, fraction, order
NOT: /A/Write all of the numbers as decimals having the same number of places. /B/Correct! /C/These
numbers are in order from greatest to least. /D/Write all of the numbers as decimals having the same number
of places.
39. ANS: A
Line up the decimal points. Add. Estimate both numbers, and add to check whether your answer is
reasonable.
KEY: addition, decimal
NOT: /A/Correct! /B/Check the position of your decimal point. /C/Check your addition and the position of
the decimal point. /D/Check your addition.
40. ANS: C
Line up the decimal points. Subtract. Estimate both numbers and subtract to check if answer is reasonable.
KEY: decimal, subtraction
NOT: /A/Did you perform the correct operation? /B/Did you perform the correct operation? /C/Correct!
/D/Check your subtraction.
41. ANS: D
Multiply the numbers.
The number of decimal places should equal the sum of the decimal places in both factors.
KEY: decimal, integers, multiplication
NOT: /A/Check for an error in your multiplication, and check the position of the decimal point. /B/Is there a
mistake in adding the numbers in the multiplication process? /C/What is the total number of decimal places in
the two factors? Correct the position of the decimal point. /D/Correct!
42. ANS: B
Multiply the numbers.
The number of decimal places should equal the sum of the decimal places in both factors.
KEY: decimal, multiplication
NOT: /A/Check for errors in your multiplication. /B/Correct! /C/Check for errors in your multiplication, and
check the position of the decimal point. /D/What is the total number of decimal places in the two factors?
Correct the position of the decimal point.
43. ANS: A
Divide the decimal by the integer.
The decimal place is placed directly above the decimal point that is under the division symbol. Estimate to
check whether your answer is reasonable.
KEY: decimal, division, integers
NOT: /A/Correct! /B/Check your math./C/The correct operation is division. /D/Which number is the
dividend, and which is the divisor?
44. ANS: A
Multiply both numbers by the least power of ten that will make the divisor an integer. The decimal point for
the answer will then go directly above the decimal point that is under the division symbol.
KEY: decimal, division
NOT: /A/Correct! /B/Check your decimal point position. /C/Check the sign of your answer. /D/Check your
decimal point position and the sign of your answer.
45. ANS: B
Multiply both numbers by the least power of ten that will make the divisor an integer. The decimal point for
the answer will then go directly above the decimal point that is under the division symbol.
KEY: decimal, division, integers
NOT: /A/Is your sign correct? Check the position of your decimal point. /B/Correct! /C/Check the position of
your decimal point. /D/Is your sign correct?
46. ANS: D
Write the integer as a fraction with 1 as the denominator. Multiply, then simplify.
1
3
=
8
3
KEY: fraction, multiplication
NOT: /A/Pay attention to your sign. /B/Do not divide the integer. /C/Do not divide the fraction. /D/Correct!
47. ANS: C
Multiply the numerators and the denominators. Then simplify.
KEY: fraction, multiplication
NOT: /A/Are you performing the correct operation? /B/Did you multiply the numerator of one fraction times
the numerator of the other? /C/Correct! /D/Did you multiply the denominator of one fraction times the
denominator of the other?
48. ANS: A
Change any mixed numbers to improper fractions, and then multiply. Simplify the answer.
KEY: mixed number, multiplication
NOT: /A/Correct! /B/Do you want to multiply by the reciprocal of the first or second fraction? /C/Is your
numerator and denominator correct? /D/Do you want to divide the fractions?
49. ANS: D
Multiply the first fraction by the reciprocal of the second.
KEY: division, fraction
NOT: /A/Are you performing the correct operation? /B/Division is the same as multiplying by what? /C/Are
your numerator and denominator correct? /D/Correct!
50. ANS: A
Write any mixed numbers as improper fractions, and then multiply the first fraction by the reciprocal of the
second. Simplify.
KEY: division, mixed number
NOT: /A/Correct! /B/Are you performing the correct operation? /C/Division is the same as multiplying by
what? /D/Are your numerator and denominator correct?
51. ANS: A
Add or subtract the numerators and keep the common denominator.
KEY: addition, fraction, like denominators, subtraction
NOT: /A/Correct! /B/Should you add the denominators? /C/Pay attention to the signs. /D/Pay attention to the
operation being performed.
52. ANS: C
Find the common denominator of the two fractions and then add or subtract.
KEY: addition, fraction, subtraction, unlike denominators
NOT: /A/Pay attention to the signs. /B/Pay attention to the operation being performed. /C/Correct! /D/Should
you add the denominators?
53. ANS: B
Add the integers and add the fractions.
KEY: addition, mixed number
NOT: /A/Watch your addition. /B/Correct! /C/Should you add the denominators? /D/Should you add the
denominators?
54. ANS: B
Write the mixed numbers as improper fractions. Then rewrite the fractions with common denominators and
subtract. Simplify the result.
KEY: mixed number, subtraction
NOT: /A/Watch your subtraction. /B/Correct!/C/Should you add the denominators? /D/Should you subtract
the denominators?
55. ANS: D
Place the percent in the numerator of a fraction, put 100 in the denominator, and simplify the resulting
fraction.
KEY: fraction, percent
NOT: /A/You found the decimal value, not the fraction. /B/Any percent less than 100 will result in a fraction
less than 1. /C/Which number goes in the numerator of the fraction? /D/Correct!
56. ANS: B
Divide the percent by 100. This is the same as moving the decimal point two places to the left.
KEY: decimal, percent
NOT: /A/Which number goes in the numerator of the fraction? /B/Correct! /C/How many places do you
move the decimal point when converting from a percent to a decimal? /D/Is this in decimal form?
57. ANS: C
Multiply the decimal by 100 and add the % symbol. This is the same as moving the decimal point two places
to the right.
KEY: decimal, percent
NOT: /A/By what number do you multiply?/B/Which direction do you move the decimal point when
converting from a decimal to a fraction? /C/Correct! /D/Should your answer be a fraction?
58. ANS: D
Divide the numerator by the denominator, multiply the result by 100, and put the % symbol after the answer.
KEY: fraction, percent
NOT: /A/How do you convert a decimal to a percent? /B/Be sure to write the answer as a percent, not a
decimal. /C/How do you convert a fraction to a decimal? /D/Correct!
59. ANS: D
Find a fraction that is close in value to the percent. Change the number to a compatible number that is easy to
use. Multiply the fraction by the compatible number.
KEY: estimate, fraction, percent
NOT: /A/Be careful when deciding which fraction and which compatible number to use. /B/Use compatible
numbers that are close to the exact numbers. /C/Remember you are dealing with percentages. /D/Correct!
60. ANS: D
Method 1:
Use the decimal equivalent of the percent to solve this problem. 0.95 195 = 185.25.
Method 2:
Set up and solve the proportion
.
KEY: percent
NOT: /A/Are you supposed to find a number or a percent? /B/Check how you setup your proportion./C/Be
careful when writing a percent as a decimal or when solving a proportion. /D/Correct!
61. ANS: D
Set up the proportion
, and solve for n.
KEY: percent
NOT: /A/Check the setup of your proportion. /B/Which numbers go in the denominators of the fractions in
the proportion? /C/Did you forget to factor in 100? /D/Correct!
62. ANS: C
Use a proportion.
Solve
for x.
KEY: percent
NOT: /A/Start by representing the percent as a decimal. /B/Check the setup of your equation. /C/Correct!
/D/Did you forget to represent the percent as a decimal?
SHORT ANSWER
63. ANS:
a. 0.80
b.
KEY: percent
64. ANS:
a. 5.02, 5.2, 5 , 5.333, and 5
b.
5 = 5.4
5.2 = 5
5.02 = 5
5 = 5.25
5.333 = 5
KEY: compare, convert, decimal, fraction, order, Performance Assessment
65. ANS:
Solution:
Write the percent as a fraction with a
denominator of 100:
Simplify the fraction:
KEY: fraction, percent
ESSAY
66. ANS:
Since you know the percent of air and the amount of air, set up a proportion:
Substitute the values you know and solve for the TOTAL air.
KEY: percent, Performance Assessment
67. ANS:
No.
You have to know how much money is currently in each account, how much money was originally deposited
in each account, and how long ago it was deposited.
KEY: interest, simple interest
68. ANS:
Percent increase.
Subtract the tree’s original height from its new height. Divide the difference by the original height and
multiply by 100 to get the percent change.
KEY: percent change, percent decrease, percent increase